When I lived in SF I had a bike, so I can contrast:
Owning a bike:
+ You can leave whenever you want, never have to worry about a bike being available
+ You know the maintenance condition of your particular bike
+ Your bike will almost certainly be lighter
- You have to carry a bike lock (or locks with you)
- You have to maintain your bike
- You have to either bring it with you, or lock it somewhere secure
- There are no secure outdoor spots for your bike (for the most part)
- In SF, inevitably, unless your bike is indoors at both ends of the trip, someone will either a) steal your bike or b) steal _parts_ of your bike, possibly preventing you from riding it away
Bike Share:
+ Once your trip is done, you can forget (not worry) about the bike
+ You don't have to maintain a bike, have bike tools, spare tires, etc.
+ You don't need to have or carry a bike lock with you
+ You can go on an all-day or overnight trip e.g., ride to BART, take a flight or Caltrain and spend the day on the peninsula. Very risky to do this usually with locking your bike up (there are steel bike boxes / lockers at some stations though)
- You may not know what kind of shape the bike is in maintenance-wise (for the most part good, but some misaligned shifters and other minor nuisances)
- You may get to a rack and find no bikes there (This has only happened once in 3 months)
- You may get to a rack and not be able to remove a bike, or only find broken bikes (this has only happened once in 3 months also)
These are largely non-hypothetical - While living here I had my bike seat stolen and the thieves had attempted to steal the handlebars but were apparently interrupted.
My previous bike actually survived being overnight in the Mission once or twice and I later discovered saw marks on the U-Lock.